However, gambling games are not statistically sound. Because of various factors you as the operator stand additional advantages such that house profit margin will likely settle to well above the house edge %. These factors include:
* players' behavioral & psychological shortcomings (they tend to lose much more than win)
* house's larger bank (you won't go bankrupt while players will, destroying their chance to get paid back by variance)
* house's more precisely followed money management
These are the reasons why even a gambling operation with 0% house edge and as large bank and yours is feasible.
That said, I must give you relief and disclose I'm absolutely the worst case of gambler's fallacy you have ever seen! If the statistical arguments eventually fail, I'm equipped to go into metaphysical discussion including the collapse of wave function and the significant role of conscious observer in the actualization of probabilities for seemingly random events. To top that off we'll not be limited of the probabilities of future events, but would discuss the observer dependent probability of past events (which is not 1 when we get into quantum physics) However, the place for that is not here.